CSc 2262 Numerical Methods

Fall 2004


Schedule: TTh 9:10-10:30 am                                         Room: Prescott 114

Instructor: Donald H. Kraft                                    Office: 286 Coates                             Phone: 578-2253

Office Hours: TTh 10:30am-Noon                                      Email:


Text: Atkinson and Han, Elementary Numerical Analysis, 3rd edition, John Wiley & Sons, Inc., 2004


Leader, Numerical Analysis and Scientific Computing, Pearson, 2004

                Schilling and Harris, Applied Numerical Methods for Engineering Using Matlab and C, Brooks/Cole, 2000

                Chapra, Applied Numerical Methods with Matlab for Engineer and Scientists, Addison-Wesley, 2005

Chapra and Canale, Numerical Methods for Engineers with Software and Programming Applications, 4th

edition, McGraw-Hill, 2002

                Heath, Scientific Computing An Introductory Survey, 2nd edition, McGraw-Hill, 2002

                Mathews and Fink, Numerical Methods Using Matlab, 4th edition, Pearson Prentice Hall, 2004

Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press,

In addition, there are journals with articles of interest, including the ACM Transactions on Mathematical Software. Also, check out       

Abstract: The course will cover computer-oriented methods for solving numerical problems in science and engineering, including finding roots (including iterative solutions such as Newton’s method), interpolation and approximation (including curve fitting), numerical integration and differentiation (including Simpson’s rule), solving linear equations (including linear algebra), solving differential equations (including Euler’s method), and, possibly, optimization and simulation.  There will be a bit of numerical analysis, i.e., the mathematics and theory behind the numerical methods (including floating point arithmetic, errors, stability, convergence, Taylor‘s series, explicit and implicit methods, and possibly, finite differences), plus a short discussion of history leading to the current interest in scientific computing.

Prerequisites:  Math 1552; CSc 1251 or CSc 1351 or CSc 2290


Midterm Exam

Final Exam


Class Participation





                No late work will be accepted. Make-up exams will not be given. Exceptional cases, such as illness or accidents, will be handled on an individual basis (instructor must be notified prior to the due dates or tests of the problem and proof presented - otherwise a score of zero will be given). Students will have one week from the date an assign­ment or homework or test is returned to seek corrections on the grading. After that time, no changes will be made to scores. All assignments will be due on a specific date and must conform to the usual programming guidelines discussed in previous CSc courses (e.g., proper header, inline documentation, structured/disciplined programming). All cases of plagiarism or excessive collaboration on assignments or tests will be treated as academic dishonesty.

                The homework will be assigned from time to time.  The source code listing and output are due at the beginning of the class period on the due date noted on the assignment.  With the exception of one or more assignments in Matlab, the programs can be done in the C programming language (you must obtain prior permission of the instructor for use of other programming languages).

Topics to be covered include*ö:

I.                     Introduction                                                              Aug 24-Sept 7

A.      History – Mathematics, Scientific Computing

B.       Mathematical Foundations

1.                    Data Representation and Conversion Text, Appendix E

2.                    Floating Point Numbers Text, Chap. 2

3.                    Rounding and Chopping Text, Chap. 2

4.                    Errors – Sources, Noise, Propagation,

Uncertainty Text, Chap 2

5.                    *Summation Text, Chap. 2

6.                    Mean Value Theorems Text, Appendix A

7.                    *Formulae

 – Algebra, Geometry, Trig, Calculus Text, Appendix B

8.                    Taylor Series Text, Chap. 1

9.                    *Commercial Packages Text, Appendix C,,,,,,,,

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10.                 Matlab Text, Appendix D

II. Roots                   Text, Chap. 3           Sept 9-21

A.     Bisection (Bracketing)

B.      *False Positioning

C.      Newton’s Method (Newton-Raphson)

D.      *Bairstow’s Method

E.       Secant Method

F.       Fixed Point Iteration

G.      *Ill-Behaved Functions

H.      *Multiple Roots

     III. Interpolation and Approximation                      Text, Chap. 4                   Sept 23-Oct Oct 12

Fall Holiday                                                                                                                                          Oct 7

A.     Polynomial Interpolation

 (Lagrangian Polynomials, Piecewise Linear Interpolation)

B.      Fourier Approximation

C.      Spline Function Interpolation

D.      *Best Approximation  (Minimax)

E.       Chebyshev Polynomials

F.       *Near-Minimax Approximation

G.      Least-Squares Approximation

H.      *Approximating Trigonometric Functions (Curve Fitting)

Midterm Exam                                                                                                                                     Oct 14

IV.                 Numerical Integration and Differentiation           Text, Chap. 5          Oct 19-Oct 28

A.     Trapezoid Rule - Integration

B.      Simpson Rule - Integration

C.      Gaussian Integration (Gauss-Jordan)

D.      *Newton-Cotes and Romberge Integration

E.       Differentiation

V.                   Linear Equations                            Text, Chap. 6          Nov 2-11

A.     Systems of Linear Equations

B.      Matrix Arithmetic

C.      Gaussian Elimination (Gauss-Seidel)

D.      LU Factorization (Decomposition, Matrix Inversion)

E.       Iteration Methods

F.       *Least Squares Data Fitting                                                                           Text, Chap. 7

G.      *Eigenvalue Problems                                                                               Text, Chap. 7

H.      *Nonlinear Systems                                                                                 Text, Chap. 7

I.        Newton’s Method

J.        General Newton Method

K.      Modified Newton Method

VI. Ordinary Differential Equations (ODE)                                  Text, Chap. 8                   Nov 16-23

A.      General Theory of Differential Equations

B.       Euler’s Method

C.       Stability and Implicit Methods

D.      Taylor and Runge-Kutta Methods

E.       Multistep Methods

F.       Systems of Differential Equations

G.       *Finite Difference Method – Two Point Boundary Value Problems

Thanksgiving Holiday                                                                                                                  Nov 25

VII. *Partial Differential Equations (PDE)                                   Text, Chap. 9                   Nov 30-Dec 2

A.      Poisson Equation

B.       One-Dimensional Heat Problem – Discretization

C.       One-Dimensional Wave Equation

VIII. *Optimization

A.      One-Dimensional

B.       Multidimensional

C.       Constrained Optimization

D.      Monte Carlo Simulation

IX. *Applications                                                                                                                                                Dec 2

Final Exam                                                                                                            Thursday, December 9, 7:30-9:30 AM


Notes: See



* The asterisk implies optional material as time permits.

öThis symbol implies free software at the website.